Your interruptions seem a bit too frequent. Who is your provider? Have you spoken to them?. How long is your outstanding contract? - often ISP's will insist you buy out the contract if you decide to switch - which is why I am on a one month rolling contract.
It could be a number of things, from the phone line, your router, or the ISP, so ideally these should be narrowed down. I had such a problem for a while after buying a new router, but it seems to have settled down now and I never did find out if it was my ISP or the router!